We are now ready to define our \(T\) -adic splitting functions. Recall from [1]} that there is a functorial embedding of \(\mathbb {Z}_p\) -modules
\(W(A) &\rightarrow 1+tA\llbracket t\rrbracket \\a &\mapsto \prod _{j = 0}^\infty E(a_i t^{p^i}).\) 
